Multi-lecto Atos-Heliu He - se s H but with Z He - electos. No exct solutio of.. but c use H wve fuctios d eegy levels s sttig poit ucleus sceeed d so Zeffective is < sceeig is ~se s e-e epulsio fo He, we ll look t e-e epulsio. Fo highe Z, we ll cll it sceeig electos e ideticl pticles. Will theefo obey Puli exclusio ule c t hve the se qutu ubes. his tus out to be due to the syety of the totl wve fuctio P46 - Heliu
P46 - Heliu chod. q. Fo He hve kietic eegy te fo both electos let the e-e itectio be fo ow esy to show the tht oe c the septe vibles d the wvefuctio is: whee these e ideticl sigle pticle wvefuctios ~tht fo Hydoge defie fot. is pticle s s positio d, e the qutu ubes fo tht eigefuctio h h, o o o
Ideticl Pticles Pticles e epeseted by wve pckets. If pcket A hs ss.5 Me, spi/, chge -, the it is electo A y wve pcket with this fetue is idistiguishble t>t t>t c t elly tell the blue fo the get pcket fte they ovelp P46 - Heliu 3
Ideticl Pticles Cete wve fuctio fo pticles the wys of kig the wvefuctio e degeete--they hve the se eegy--d c use y lie cobitio of the wvefuctios Wt to hve wvefuctio whose pobbility tht is ll esued qutities is the se if d e flipped * * * hese e NO the se. Isted use lie cobitios s degeete. Hve syetic d tisyetic cobitio A A [ [ A * P46 - Heliu 4 ] ] uchged
Ideticl Pticles i Box Cete wve fuctio fo pticles i box πx πx cos o si qutu A A[cos A[cos sttes πx πx si : si πx πx cos cos si si the tisyetic te if eithe both pticles e i the se qutu stte OR if xx suppessio of ANI whe pticles e close to ech othe. hceet of YM whe two pticles e close to ech othe this gives diffeet vlues fo the vege septio < x-x > d so diffeet vlues fo the dded te i the eegy.o diffeet eegy levels fo the ANI d YM wve fuctios the degeecy is boke, πx πx πx πx ] ] P46 - Heliu 5
P46 - Heliu 6 Apply syety to He he totl wve fuctio ust be tisyetic but hve both spce d spi copoets d so choices: hve spi / pticles. he totl is o is spi-syetic is spi-tisyetic sy tisy OR tisy syetic eithe spi spce spi spce spi spce He ± ± s s s spi
He sptil wve fuctio hee e syetic d tisyetic sptil wvefuctios which go with the ti d sy spi fuctios. Note,b e the sptil qutu ubes,l, but ot spi spce spce sy sy b b b b whe the two electos e close to ech othe, the tisyetic stte is suppessed goes to if exctly the se poit. Likewise the syetic stte is ehced --> xchge Foce spi stte hs the electos o vege futhe pt s tisyetic spce. o slle epulsive potetil d so lowe eegy ote if b, se spce stte, ust hve pove Puli exclusio P46 - Heliu 7
He egy Levels tes i chod. q.: e 4πε e 4πε 4πε Oth ppoxitio. Igoe e-e te. 4 3.6e, Fist ppoxitio: look t expecttio vlue of e-e te which will deped o the qutu sttes I,j of the electos d if o 68 9 7 e e e e 4 3.6e ij ij ij with ij e 4πε P46 - Heliu 8
He egy Levels Fo goud stte, ptil stte is syetic d. he <> is esued to be 3 e ---> goud-93-79 e Fo,. C hve L,. C hve eithe o. he syeticl sttes hve the electos close ----> lge <> d lge L d L hve diffeet dil wvefuctios. he, L hs oe ovelp with the,l stte --> electos e close --> lge <> d lge N L P N L N L P46 - Heliu 9
He egy Levels -7 N, L,L -7 N, L,L -, P46 - Heliu